An L^1 Ergodic Theorem for Sparse Random Subsequences

Details An L^1 Ergodic Theorem for Sparse Random Subsequences An L^1 Ergodic Theorem for Sparse Random Subsequences

2008-12-16

arxiv.org/abs/0812.3175v1

Math. Res. Lett. 16 (2009), no. 5, 849-859

Mathematics

Dynamical Systems

LaTeX, 9 pages

Scientific paper

We prove an L^1 subsequence ergodic theorem for sequences chosen by
independent random selector variables, thereby showing the existence of
universally L^1-good sequences nearly as sparse as the set of squares. In the
process, we prove that a certain deterministic condition implies a weak maximal
inequality for a sequence of \ell^1 convolution operators.

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